Analysis of Variance II
Checking ANOVA
Assumptions
Lec20.Exxon.R
ExxonOil.csv
Poplar.R
Methods for Communicating
Statistical Information
Confidence Intervals
How confident are we in the estimates
we have?
Hypothesis Tests
Can we reject the null hypoth

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Lab 3
Name:
Section:
Date:
Lab 3 will focus on using R scripts to organize and apply commands. Scripts are
files that contain commands that can be executed in part v

Multiple Comparisons
Reference:
Steel and Torrie, 1980, Principles and
Procedures of Statistics, McGraw/Hill
Lec21.Clover.R
Red clover: Trifolium pratense
Vermont state flower
http:/www.50states.com/flower/vermont.htm
Rhizobium trifolii
Appl Environ Micro

Bayesian Statistics I
Concept by Example
Let us suppose we have 5 scientists each
analyzing the same 100 observations. Let
us suppose the purpose of the experiment
is to determine the probability that a certain
genetic effect will take place in the next
g

Multisample Hypotheses
Analysis of Variance
Sources of Variation
Multiple Comparisons
Devore and Berk Chapter 11
Lec19.ANOVA1.R
Motivation
Thus far weve examined measuring
differences between one sample and
another
Examples:
Experimental
Treatment and Con

Nonparametric Statistics
D&B Chapter 14
Alternative Approaches
Advantages
More flexible relative to shape of the
distribution doesnt have to be
normal
Can often be applied to categories (e.g.
sex, major, college, university)
Simple
Outliers have less of a

Bayesian Methods
MCMC
Bayes Theorem
P( A, B)
P( B | A) =
P( A)
P( A | B) P( B)
=
P( A)
P( A | B) P( B)
=
P( A | B) P( B)
Bayes Theorem
P( A | B) P( B)
P( B | A) =
P( A)
P( A | B) P( B)
Gaussian Probability Density
( X )
P( X | ) =
exp
2
2
2
2
2
X ~ N

Exercise 1
A Cornell student believes the average
length (C) of commercial breaks on
cable channels (ESPN, TNT, etc.) is
longer than the average length (N) of
commercial breaks on the networks
(ABC, CBS, NBC). She times a random
sample of commercials from

Categorical Data
(Data representing counts by
categories)
Population Proportion
Chi-Square Goodness of Fit
Contingency Tables
Single Slide Review
Are populations the same or different?
Check means
Check variances
Analyze mean squared error under
different

In God we trust
All others bring data!
"Over the last fifty years, How to Lie
with Statistics has sold more copies
than any other statistical text." J.M.
Steele. "Darrell Huff and Fifty Years
of How to Lie with Statistics. Statistical
Science, 20 (3), 20

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Lab 2
Name:
Section:
Date:
In Lab 1 we became familiar with different ways of reading data into R, computing
some standard statistics based on that data, and examini

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 6
Name:
Section:
Date:
As an alternative to the use of fathers height to predict sons height, Galton used the
midparent height; the average of the fathers a

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 3 (25 points)
Name:
Section:
Date:
Objectives:
i.
ii.
iii.
Explore methods for computing probabilities.
Determine how normal a random set of binomial values

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 5
Name:
Section:
Date:
In an effort to link cold environments with hypertension in humans, a preliminary
experiment was conducted to investigate the effect

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 2 (25 points total)
Name:
Section:
Date:
Objectives:
i. To demonstrate an understanding of basic probability concepts.
ii. To straightforwardly characterize

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 4
Name:
Section:
Date:
This weeks homework is based upon the data below which are available on the
course website (scrubber.csv). (Note that it has a header

Bayes Formula
Discrete Probability Distributions
Devore and Berk
Section 2.4 (conditional probability)
Sections 3.1, 3.2, 3.3 (random variables)
Sections 3.5, 3.6, 3.7 (distributions)
We will do more with Bayes later (Sec 14.4)
Conditional probability
A
B

Visualizing Data
Devore and Berk Chp 1
Visualizing Quantitative Data,
Tufte E. R., Graphics Press, 2001
Graphical Methods for Data Analysis,
Chambers J., Cleveland, B. Kleiner,
and P. Tukey, Duxbury Press, 1983
Exploratory Data Analysis,
Tukey J., Addison

The Normal Distribution
Also Known As
The Gaussian Distribution
Devore and Berk Sections
4.1, 4.3, 4.6
But first a recap:
Observation
Analysis
Understanding
Judgment
Action
20
10
0
Observation
Analysis
Understanding
Judgment
Action
30
100 people each flip

Probability and
Probability and
Statistics
Statistics
Devore and Berk Chapter 2
Independent Observations
What is the chance of
an event happening?
Winning the toss of a coin?
Getting 4 aces in 5 card poker hand?
Having blue eyes if one parent has
blue

Biological Statistics I
BRTY 3010 / NTRES 3130 /STSCI 2200
Fall 4 credits
Lecture: T and Th 8:40 - 9:55
Bradfield
Instructor: 101
Dr. Patrick J.
Labs: M 12:20-1:10, 1:25-2:15, 2:30-3:20, 3:35-4:25
Sullivan
W 2:30-3:20, 3:35-4:25
204 Fernow Hall
Mann 30 (A

Biological Statistics I
Biometry 3010 / Natural Resources 3130 / Statistical Science 2200
Homework 1 (25 points total)
Name:
Section:
Date:
Objectives:
i. To learn how to visualize the information contained in data.
ii. To identify quantitative and visual